Problem: Simplify to lowest terms. $\dfrac{30}{50}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 50? $30 = 2\cdot3\cdot5$ $50 = 2\cdot5\cdot5$ $\mbox{GCD}(30, 50) = 2\cdot5 = 10$ $\dfrac{30}{50} = \dfrac{3 \cdot 10}{ 5\cdot 10}$ $\hphantom{\dfrac{30}{50}} = \dfrac{3}{5} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{30}{50}} = \dfrac{3}{5} \cdot 1$ $\hphantom{\dfrac{30}{50}} = \dfrac{3}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{50}= \dfrac{2\cdot15}{2\cdot25}= \dfrac{2\cdot 5\cdot3}{2\cdot 5\cdot5}= \dfrac{3}{5}$